Pragmatic trellis coded modulation (PTCM) has become popular because it allows a common basic encoder and decoder to achieve respectable coding gains for a wide range of bandwidth efficiencies (e.g. 1-6 b/s/Hz) and a wide range of higher order coding applications, such as 8-PSK, 16-PSK, 16-QAM, 32-QAM, etc. For lower order coding applications, such as QPSK or BPSK, PTCM offers no advantage because quadrature, complex communication signals provide two dimensions (i.e. I and Q) per unit baud interval with which to convey two or fewer symbols per unit interval.
In general, PTCM employs primary and secondary modulation schemes. The words "primary" and "secondary" do not indicate relative importance. Rather, the primary modulation is simply applied to a first set of information bits, and the secondary modulation is applied to a second set of information bits. The first set of information bits is phase mapped so that it perturbs the phase constellation to a greater degree than the second set of information bits. Conventionally, the secondary modulation scheme differentially encodes its subset of information bits, then encodes these differentially encoded bits with a strong error detection and correction code, such as the well known K=7, rate 1/2 "Viterbi" convolutional code (i.e. Viterbi encoding). The primary modulation scheme need do no more than differentially encode its subset of the information bits. The resulting symbols from the primary and secondary modulation schemes are then concurrently phase mapped to generate quadrature components of a transmit signal. The symbol data are conveyed through the phase and amplitude relationships between the quadrature components of the transmit signal.
Conventional pragmatic coding schemes phase map at least two secondary (i.e. convolutionally encoded) bits per unit baud interval with at least one primary (i.e. not convolutionally encoded) bit per unit baud interval. This produces markedly improved bit error rate (BER) performance in the face of increasing signal-to-noise ratio (e.g. energy per bit divided by noise, or E.sub.b /N.sub.o), particularly for higher coding rates, such as rate 5/6, 8-PSK, rate 8/9, 8-PSK, and the like. The coding rate (e.g. 5/6, 8/9, etc.) provides one indication of coding gain. In a rate 5/6 encoder, five user information bits are provided to the encoder for each six symbols generated by the encoder; and, in a rate 8/9 encoder, eight user information bits are provided to the encoder for each nine symbols generated by the encoder. Higher coding rates are desirable because more user information is communicated in a given time interval than with lower coding rates, all other parameters being equal.
FIG. 1 shows a curve 10 that illustrates typical conventional pragmatic, higher code rate, BER performance as a function of signal-to-noise ratio when at least two secondary bits per unit baud interval are mapped with at least one primary bit per unit baud interval. In short, the steep slope to the right of the curve 10 "knee" indicates that small improvements in E.sub.b /N.sub.o yield massive improvements in BER. In order to achieve a very good BER, only a modest signal-to-noise ratio is required. However, the signal-to-noise ratio required to deliver only a modest BER is higher than desired, particularly at higher coding rates.
Another data communication coding technique that has become popular is concatenated coding. With concatenated coding, an inner code need deliver only a modest BER to an outer code, which then typically improves this modest BER by several orders of magnitude. In a typical scenario, an inner code may deliver a BER of 10.sup.-4 or better to an outer code, which then improves the overall BER to around 10.sup.-12. The outer code is typically provided through a block encoding/decoding scheme, such as the well known Reed-Solomon code. The inner code is typically provided through a convolutional encoder/decoder, such as the well known rate 1/2 Viterbi code. A common basic encoder and decoder can be used for a wide range of higher order coding applications when a pragmatic inner code is used.
When a pragmatic inner coding scheme is used, it desirably provides only the modest BER required by the outer coding scheme. Lower error rates than this modest BER do not lead to improved overall BER from the outer coding scheme. Rather, they are achieved at a cost of operating transmitters at higher power levels than required and at a cost of transmitting excessive energy which can interfere with the operation of adjacent communication channels. Unfortunately, this modest BER tends to be achieved by conventional pragmatic inner coding schemes that map at least two secondary bits per unit baud interval with at least one primary bit per unit baud interval at an undesirably high signal-to-noise ratio.
Carrier-coherent receiving schemes are often used with concatenated codes and with pragmatic codes because they demonstrate improved performance over differentially coherent receiving schemes. Coherent receivers become phase synchronized to the received signal carrier in order to extract the amplitude and phase relationships indicated by the quadrature components. However, an ambiguity results because the receiver inherently has no knowledge of an absolute phase reference, such as zero. In other words, for M-PSK where one of 2.sup.K possible phase states are conveyed during each unit interval, where K equals the number of symbols conveyed per unit interval, then the receiver may identify any of the 2.sup.K phase states as the zero phase state. This ambiguity must be resolved before the conveyed amplitude and phase data successfully reveal the information bits.
Conventionally, the differential encoding is applied to information bits at the modulator and differential decoding used in the demodulator to at least partially resolve the phase ambiguity. After the secondary modulation is decoded in the demodulator, the decoded secondary bits are then used to decode the primary modulation in a way that partially resolves the ambiguity.
However, the use of differential encoding is undesirable in resolving rotational ambiguity because when a single error occurs, two highly correlated errors are observed in the decoder. Consequently, a significant degradation of error probabilities results and BER suffers.
Accordingly, a need exists for a coding scheme which delivers a modest BER at a lower signal-to-noise ratio than required by conventional pragmatic inner coding schemes that map at least two secondary bits per unit interval with at least one primary bit per unit interval. Moreover, a need exists for a technique for resolving phase ambiguities without differentially encoding the user information.